1. Field of the invention
The present invention relates to a noise shaper, and more particularly to a stable noise shaper of a small circuit scale capable of maintaining a high precision even if an oversampling ratio is lowered by having a higher order (specifically, a third order or more).
2. Description of related art
For example, one typical conventional noise shaper comprises first and second integrators, a quantizer having its input connected to an output of the second integrator and outputting a one-bit signal, and a feedback circuit for feeding back an output of the quantizer to the first and second integrators. In operation, the first-stage integrator receives and integrates a difference signal between a one-sample delayed signal, outputted from the quantizer, and an input signal, and the second-stage integrator receives and integrates a difference signal between the output signal of the first-stage integrator and a double of the one-sample delayed signal outputted from the quantizer. The output of the second-stage integrator is inputted to the quantizer. At this time, if the input of the quantizer is larger than "0", "+1" is outputted, and if it is smaller than "0", "-1" is outputted.
Here, assuming that a quantization noise generated in the quantizer is "Q", there is a relation between an input signal X and an output signal Y of the noise shaper, shown by the following formula: EQU Y(z)=X(z).z.sup.-2 +(1-z.sup.-1).sup.2.Q(z)
Consequently, an output spectrum of the noise shaper is a spectrum formed by superposing a signal obtained by the second-order differentiation of the quantization noise on the input of the noise shaper. Namely, the quantization noise is shaped and superposed in a high frequency region, so that the sum of the noise in a signal band is remarkably reduced. Thus, the higher the oversampling ratio becomes, the noise in the band is much reduced. A S/N ratio is represented by the following formula: EQU (S/N).sub.max =15.pi..theta./2(.theta.=2.pi.f.sub.B /f.sub.s)
where f.sub.B and f.sub.S represent a signal band and a sampling frequency, respectively.
The noise shaper described above is a so-called second-order noise shaper. For example, if it is desired to obtain a resolution of 16 bit precision in this noise shaper, an oversampling ratio of about 256 times is required.
If the oversampling ratio is high, for example, in the case of a digital noise shaper, it is required to reduce the operation time. Thus, both the electric consumption and the circuit-scale increase. In the case of using the noise shaper as an A/D (analog-to-digital) converter, it is required to speed up an operational amplifier, which is one constituent of the noise shaper, so that both the electric consumption and the circuit-scale also increase. Then, in order to reduce the oversampling ratio while achieving a desired S/N (signal/noise) characteristics, a process of using a multi-value output quantizer instead of a "1-bit" output quantizer and a process of increasing the order of the noise shaper have been proposed.
In the process of causing the quantizer to have a multi-value, for example, in the case of the digital noise shaper, the output of the quantizer before a multi-value so, that a D/A (digital-to-analog) converter located at the subsequent stage must be structured to have a multi-value input. On the other hand, in the case of a so-called multi-bit D/A converter having a multi-value input, the precision required for analog elements constituting the converter is severe, and in addition, has a big influence on the S/N characteristics and the distortion characteristics. Further, in the case of forming an A/D converter having a multi-value quantizer, since a feedback signal added from the output of the quantizer to the input of each of the integrators in the above mentioned conventional noise shaper is an analog value, the characteristics of the AID converter depends on that of the D/A converter required in this part, so that it is difficult to obtain a high precision.
Accordingly, in order to obtain a desired high precision characteristics by lowering the oversampling ratio, a process of making the noise shaper the third order or more is generally effective. However, it has been known that the system becomes unstable if the noise shaper is made the third order or more. Here, stability of a typical third-order noise shaper will be examined. The typical third-order noise shaper comprises first, second and third integrators, a quantizer having its input connected to an output of the third integrator and for outputting a one-bit signal, and a feedback circuit for feeding back the output of the quantizer to the first, second and third integrators. The integrators am composed of a digital circuit.
In operation, the first-stage integrator receives and integrates a difference signal between a one-sample delayed signal, outputted from the quantizer, and an input signal. Further, the second-stage integrator receives and integrates a difference signal between an output signal of the first-stage integrator and a triple of the one-sample delayed signal outputted from the quantizer. Furthermore, the third-stage integrator receives and integrates a difference signal between an output signal of the second-stage integrator and a triple of the one-sample delayed signal outputted from the quantizer. The output of the third-stage integrator is inputted to the quantizer. At this time, if the input of the quantizer is larger than "0", "+1" is outputted, and if it is smaller than "0", "-1" is outputted. In the noise shaper having the structure as mentioned above, and assuming that the quantization noise generated in the quantizer is "Q", them is a relation between an input signal X and an output signal Y of the noise shaper, shown by the following formula: EQU Y(z)=X(z).z.sup.-1 +(1-z.sup.-1).sup.3.Q(z)
Consequently, an output spectrum of the noise shaper is a spectrum formed by superposing a signal obtained by the third-order differentiation of the quantization noise on the input of the noise shaper. Namely, the quantization noise is shaped and superposed in the high frequency region, so that the sum of the noise in the signal band is remarkably reduced. This effect is significantly larger than that of the second-order noise shaper. If the third-order noise shaper mentioned above operates stably, it is possible to considerably reduce the oversampling ratio which is required in order to obtain a desired S/N characteristics, and it is also possible to reduce the electric consumption and the circuit scale remarkably. Unfortunately, however, the third-order noise shaper mentioned above does not function stably. In general, in the case of discussing the system stability, it depends on whether the pole of the input/output transfer characteristics is in a unit circle on the complex plane or not. Considering the quantizer as a variable gain operational amplifier of a gain .lambda., the input/output transfer function of the third-order noise shaper mentioned above is given by the following formula: EQU Y/X=z.sup.-3 /[(z.sup.-3 -3z.sup.-2 +3z.sup.-1)..lambda.+(1-z.sup.-1).sup.3 ]
Thus, the pole is given by the formula with a denominator=0, and in the root locus having a parameter .lambda., it has a root (pole) out of the unit circle when .lambda.&lt;0.5, so that the noise shaper becomes instable.
Many architectures of the noise shaper having a third order or more have been proposed. Among them, one useful architecture has been proposed by K. C. H. CHAO et al in "A Higher Order Topology for Interpolative Modulators for Oversampling A/D Converters" "IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS", Vol. 37, No. 3, pp 309-318, March 1990. According to this structure, it is possible to modify the pole of the input/output transfer function without injuring so much the effect for shaping the quantization noise in the high frequency region, by appropriately choosing the multiplication coefficient shown in the drawing. However, it is still impossible to ensure the system stability with any value of .lambda. even at this time. In particular, a multi-input adder is also required at an input part of the rust-stage integrator and at an input part of the quantizer in this architecture. In the case of using it for a digital noise shaper, a lot of adders having a long operation word length are required. Further, if it is used for an A/D converter, an extra adder(s) using an operation amplifier is required so that the electric consumption and the circuit scale become large.
In addition, anther architecture has been proposed by L. Longo et all, in "A 13 bit ISDN-band Oversampled ADC using Two-Stage Third Order Noise Shaping", "IN PROC. 1988 CUSTOM INTEGRATED CIRCUITS CONF., pp 21.2.1-4, June 1988". In this architecture, the system stability is ensured by connecting a second-order noise shaper and a first-order noise shaper in cascade. In the case of using this architecture as a digital noise shaper, not only many adders having a long operation word length become necessary, but also the precision required for the D/A converter at the subsequent stage becomes severe because the output becomes multi-bit. Further, in the case of using it as an AID converter, an extra adder(s) using an operation amplifier is required. In addition, deterioration of the S/N characteristics or the like due to variation of the constituent elements appears remarkably because the architecture uses a method of cancelling in a digital manner a quantization error which has occurred in the quantizer.
Even in the improved third-order noise shapers as mentioned above, the following disadvantages have been encountered. Namely, in order to ensure the system stability, the circuit scale becomes extremely large, and the requirement to the analog circuit characteristics also becomes severe. In addition, it is difficult to realize the high precision characteristics.